A124346 Number of rooted identity trees on n nodes with thinning limbs.

1, 1, 1, 2, 2, 4, 6, 11, 17, 32, 56, 102, 184, 340, 624, 1161, 2156, 4036, 7562, 14234, 26828, 50747, 96125, 182545, 347187, 661618, 1262583, 2413275, 4618571, 8850905, 16981142, 32616900, 62713951, 120703497, 232527392, 448344798, 865182999, 1670884073

Offset: 1

Author

Christian G. Bower, Oct 30 2006, suggested by Franklin T. Adams-Watters

Keywords

• nonn

Comments

A rooted tree with thinning limbs is such that if a node has k children, all its children have at most k children.

Examples

			The a(7) = 6 trees are ((((((o)))))), (o((((o))))), (o(o((o)))), ((o)(((o)))), ((o)(o(o))), (o(o)((o))). - _Gus Wiseman_, Jan 25 2018
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..140

Crossrefs

Cf. A000081, A001678, A003238, A004111, A124343-A124348, A276625, A290689, A298303-A298305, A298422.

Row sums of A245120.

Programs

Mathematica

idthinQ[t_]:=And@@Cases[t,b_List:>UnsameQ@@b&&Length[b]>=Max@@Length/@b,{0,Infinity}];
itrut[n_]:=itrut[n]=If[n===1,{{}},Select[Join@@Function[c,Union[Sort/@Tuples[itrut/@c]]]/@IntegerPartitions[n-1],idthinQ]];
Table[Length[itrut[n]],{n,25}] (* Gus Wiseman, Jan 25 2018 *)